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Limit Theorems for Associated Random Fields and Related Systems

Advanced Series on Statistical Science & Applied Probability v. 10

Genres: Stochastics
Format: Hardback
Publisher: World Scientific Publishing Co Pte Ltd, Singapore, Singapore
Published: 12th May 2007
Dimensions: w 165mm h 249mm d 23mm
Weight: 946g
ISBN-10: 9812709401
ISBN-13: 9789812709400
Barcode No: 9789812709400
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).

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